Algebra Question?

Question

I'm having trouble understanding how 2x^3 -3x^2 - 3x+2 = 0
becomes (x-2) (x + 1) (2x-1) = 0 when factored. Plz help.

Answer 1

isnt it that if you factor one equation you erquating to the simplest form of the equation therefor there is no alternative explanation regarding to your question...

Answer 2

Let P(x) = 2x^3 - 3x^2 -3x +2 = 0.
We can use the factor theorem to factorise the left hand side of the equation.
Try x = -1, P(-1) = 2(-1)^3 - 3(-1)^2 - 3(-1) + 2
= -2 - 3 + 3 + 2
= 0
Since P(-1) = 0 or the expression becomes zero when x = 1, then x +1 is a factor of P(x) and we can use the long division to find out all the other factors.

2x^3-3x^2-3x+2 = 0
(x+1) (2x^2-5x+2) = 0
(x+1) (2x-1) (x-2) = 0
x+1=0, 2x-1 =0 and x-2= 0
x=-1, x=1/2 and x=2

Answer 3

There are mathematically precise ways to solve a cubic, but if you suspect it factors easily, here's what I'd do in a case like this:
For the x terms, you're looking for three factors which multiply to be 2. So basically 2, 1, and 1 are the only options, with their negative equivalents (eg 2, -1, -1, etc).
Similarly for the constant term.

That doesn't give you too many options. You know (x-2) must be a factor 'cos if you put x=2 in the equation it works
that is, 2*8-3*4-3*2+2=0.

Similarly, -1 works. So you already have (x-2)(x+1)(???)
So given that we only have 2s and 1s to play with you can get
(x-2)(x+1)(2x-1).

Hope this gives you some aid to think about other similar problems.
.

Answer 4

To factor this polynomial, you need to first find at least one of its roots. The Rational Zeros Theorem can help you find one. Let's say you find 2 as a root. Then divide the polynomial by x-2 (this must be a factor if 2 is a root) using long division. As a result, you will get 2x^2 + x - 1. This you can factor into (x+1)(2x-1).

Answer 5

2x^3 -3x^2 - 3x+2 = 0
2x^3 - 2x^2 - x^2 - 4x + x + 2 = 0
rearranging
2x^3 - 2x^2 - x^2 + x - 4x + 2 = 0
(x^2 - x)( 2x - 1) - 2( 2x - 1) = 0
(2x - 1) ( x^2 - x - 2) = 0
0r
(x^2 - x - 2)(2x - 1) = 0
(x^2 - 2x + x - 2)(2x-1) = 0
[ x ( x - 2) + 1 ( x - 2) ] ( 2x - 1) = 0
(x - 2) ( x + 1) ( 2x - 1) = 0

Answer 6

f(2) = 16 - 12 - 6 + 2 = 0-->x-2 is a factor
Use synthetic division to divide by x - 2:-
*2|2**-3**-3***2
**|****4***2***-2
**---------------
**|2**1***-1***0
f(x) = (x - 2)(2x² + x - 1)
f(x) = (x - 2) (2x - 1) (x + 1)

Answer 7

yeah use the rational root theorem douche bag